%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU152+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 08:00:59 PM UTC 2025 % Result : Theorem 3.63s 3.81s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU152+1 : TPTP v9.2.0. Released v3.3.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n018.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 04:55:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.63/3.81 SZS status Theorem for theBenchmark.p % 3.63/3.81 SZS output start Proof for theBenchmark.p % 3.63/3.81 Clause #4 (by assumption #[]): Eq (Not (∀ (A B : Iota), in A B → Eq (set_union2 (singleton A) B) B)) True % 3.63/3.81 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset (singleton A) B) (in A B)) True % 3.63/3.81 Clause #7 (by assumption #[]): Eq (∀ (A B : Iota), subset A B → Eq (set_union2 A B) B) True % 3.63/3.81 Clause #17 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (B : Iota), subset a B → Eq (set_union2 a B) B) True % 3.63/3.81 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (subset a a_1 → Eq (set_union2 a a_1) a_1) True % 3.63/3.81 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (Eq (set_union2 a a_1) a_1) True) % 3.63/3.81 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (set_union2 a a_1) a_1) % 3.63/3.81 Clause #25 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset (singleton a) B) (in a B)) True % 3.63/3.81 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Iff (subset (singleton a) a_1) (in a a_1)) True % 3.63/3.81 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton a) a_1) True) (Eq (in a a_1) False) % 3.63/3.81 Clause #34 (by clausification #[4]): Eq (∀ (A B : Iota), in A B → Eq (set_union2 (singleton A) B) B) False % 3.63/3.81 Clause #35 (by clausification #[34]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), in (skS.0 0 a) B → Eq (set_union2 (singleton (skS.0 0 a)) B) B)) True % 3.63/3.81 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (∀ (B : Iota), in (skS.0 0 a) B → Eq (set_union2 (singleton (skS.0 0 a)) B) B) False % 3.63/3.81 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.63/3.81 Eq (Not (in (skS.0 0 a) (skS.0 1 a a_1) → Eq (set_union2 (singleton (skS.0 0 a)) (skS.0 1 a a_1)) (skS.0 1 a a_1))) % 3.63/3.81 True % 3.63/3.81 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 3.63/3.81 Eq (in (skS.0 0 a) (skS.0 1 a a_1) → Eq (set_union2 (singleton (skS.0 0 a)) (skS.0 1 a a_1)) (skS.0 1 a a_1)) False % 3.63/3.81 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True % 3.63/3.81 Clause #40 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 (singleton (skS.0 0 a)) (skS.0 1 a a_1)) (skS.0 1 a a_1)) False % 3.63/3.81 Clause #42 (by superposition #[39, 27]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) True) (Eq True False) % 3.63/3.81 Clause #45 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) True % 3.63/3.81 Clause #47 (by superposition #[45, 20]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_union2 (singleton (skS.0 0 a)) (skS.0 1 a a_1)) (skS.0 1 a a_1)) % 3.63/3.81 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Eq (set_union2 (singleton (skS.0 0 a)) (skS.0 1 a a_1)) (skS.0 1 a a_1) % 3.63/3.81 Clause #49 (by clausification #[40]): ∀ (a a_1 : Iota), Ne (set_union2 (singleton (skS.0 0 a)) (skS.0 1 a a_1)) (skS.0 1 a a_1) % 3.63/3.81 Clause #50 (by forward demodulation #[49, 48]): ∀ (a a_1 : Iota), Ne (skS.0 1 a a_1) (skS.0 1 a a_1) % 3.63/3.81 Clause #51 (by eliminate resolved literals #[50]): False % 3.63/3.81 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------